Question

The numerator of a fraction is 2 less than the denominator.If 3 is added to both the numerator and the denominator,the fraction becomes ¾.Find the fraction. (explain)​

Answer 1

Given:

• Numerator of fraction is 2 less than its denominator.
• If 3 is added to both numerator and denominator the fraction becomes 3/4.

To Find :

• original Fraction

━━━━━━━━━━━━━

$\small\mathfrak{\color{red}{\underline{\underline{Answer♡}}}}$

Let the denominator of the fraction be X.

Then it's, Numerator becomes = x-2.

After adding 3 to both the numerator and denominator

• Numetator = x-2+3 = x+1.
• Denominator = x+3.

$so \: the \: fraction \: becomes \: \frac{x + 1}{x + 3}$

But, the given fraction is 3/4 .

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀( from given.)

$\frac{x + 1}{x + 3} = \frac{3}{4}$

$4x + 4 = 3x + 9$

$4x - 3x = 9 - 4$

$x = 5$

Thus,

• numerator = x-2 = 5-2 = 3
• Denominators = 5

Hence, the original fraction is 3/5.

$\red{\boxed{\bold{\large{HopeitHelps}}}}$

Answer 2

${\huge{\underline{\boxed{\red{\mathcal{Answer}}}}}}$

Given:

• Numerator of a fraction is 2 less than the denominator.
• Adding 3 to both numerator and denominator gives us 3/4.

To Find:

• The fraction

Assumption:

• Let the numerator be x, so the denominator will be (x + 2)

Solution:

$\text{We are given that,} \\:\implies \dfrac{x+3}{x+2+3} = \dfrac{3}{4} \\\\:\implies \dfrac{x+3}{x+5} = \dfrac{3}{4} \\\\:\implies 4x + 12 = 3x + 15 \\\\:\implies 4x - 3x = 15 - 12 \\\\:\implies x = 3. \\\\:\implies x = 3\:and\:x+2 = 5. \\\\\bf{:\implies Fraction = \dfrac{3}{5}}$

Hope it helps!!